For each m≥1 , u_{m}(G) is defined to be the intersection of the normalizers of all the subnormal subgroups of defect at most m in G . An ascending chain of subgroups u_{m,i}(G) is defined by setting u_{m,i}(G)/u_{m,i−1}(G)=u_{m}(G/u_{m,i−1}(G)) . If u_{m,n}(G)=G , for some integer n , the m - Wielandt length of G is the minimal of such n .
In [ 3 ], Bryce examined the structure of a finite
... [Show full abstract] soluble group with given m -Wielandt length, in terms of its polynilpotent structure. In this paper we extend his results to infinite soluble groups.
1991 Mathematics Subject Classification . 20E15, 20F22.